Let f (x) = LG (1 + 2 ^ x + A * 4 ^ x) / 3, where a ∈ R, if f (x) is meaningful when x ∈ (- ∞, 1], find the value range of A

Let f (x) = LG (1 + 2 ^ x + A * 4 ^ x) / 3, where a ∈ R, if f (x) is meaningful when x ∈ (- ∞, 1], find the value range of A

If a = 0, then the true number is always greater than 0
A is not equal to 0
x

It is proved that the function f (x) = x & # 178; + 16 / X & # 178; (x > 0) decreases in the interval (0,2)

It is proved that if X & # 178; = t, then f (T) = t + 16 / T
∵x>0
∴t∈(-∞,0)U(0,+∞)
∵ f (T) decreases on t ∈ (0, √ 16)
On X & # 178; ∈ (0,4), f (x) decreases
The decrease of F (x) in X ∈ (- 2,0) and (0,2)